M. Reinelt, K. Schmid, K. Krieger SEWG High-Z Ljubljana Max-Planck-Institut für Plasmaphysik EURATOM Association, Garching b. München, Germany Extended grid DIVIMP erosion deposition modelling

Outline Question: Steady state surface composition of the ITER first wall ? Our conceptual approach & strategy Standard and extended grids for DIVIMP Modeling of material mixing Modeling of plasma impurity generation Modeling of chemical phase formations "Work in progress" Question: Steady state surface composition of the ITER first wall ? Our conceptual approach & strategy Standard and extended grids for DIVIMP Modeling of material mixing Modeling of plasma impurity generation Modeling of chemical phase formations "Work in progress"

Motivation What are the steady state surface concentrations of the ITER first wall ? Initial surface composition Initial surface composition Plasma impurity concentration Plasma impurity concentration Erosion by hydrogen Bulk material Bulk material Temperature Re-deposition Erosion by impurities and self sputtering Deposition Plasma transport Sublimation Diffusion Phase formations Layer growth Dynamic surface composition Dynamic surface composition Steady state surface: Total flux balance Steady state surface: Total flux balance

Simplifications Assumption 1: Plasma transport is instantaneous Erosion by hydrogen Re-deposition Erosion by impurities and self sputtering Deposition INSTANT Plasma transport Sublimation Dynamic surface composition Dynamic surface composition Bulk material Bulk material Temperature Diffusion Phase formations Layer growth

Simplifications Erosion by hydrogen Temperature Re-deposition Erosion by impurities and self sputtering Deposition INSTANT Plasma transport Sublimation Diffusion Phase formations Layer growth CONSTANT bulk composition Dynamic surface composition Dynamic surface composition Assumption 1: Plasma transport is instantaneous Assumption 2: Bulk composition is constant All processes depend primarily on the concentrations in the near surface region. All processes depend primarily on the concentrations in the near surface region.

Conceptual approach DIVIMP Plasma transport of impurities Expected results: * Steady state wall concentrations & erosion fluxes * Plasma impurity concentrations Benchmark results with JET experiments Extrapolate to ITER ERODEPDIF: Flux balances ERODEPDIF: Flux balances Background plasma OEDGE (OSM) OEDGE (OSM) SOLPS (B2+Eirene) SOLPS (B2+Eirene) CARRE, recent codes CARRE, recent codes Grid Diffusion Sublimation Chemical phase formation Impurity generation SDTrim Materials properties Materials properties

Conceptual approach DIVIMP Plasma transport of impurities ERODEPDIF: Flux balances ERODEPDIF: Flux balances Background plasma OEDGE (OSM) OEDGE (OSM) SOLPS (B2+Eirene) SOLPS (B2+Eirene) CARRE, recent codes CARRE, recent codes Grid Diffusion Sublimation Chemical phase formation Impurity generation SDTrim Materials properties Materials properties

Conceptual approach DIVIMP Plasma transport of impurities ERODEPDIF: Flux balances ERODEPDIF: Flux balances Background plasma OEDGE (OSM) OEDGE (OSM) SOLPS (B2+Eirene) SOLPS (B2+Eirene) CARRE, recent codes CARRE, recent codes Grid Diffusion Sublimation Chemical phase formation Impurity generation SDTrim Materials properties Materials properties

Extended grid (EG) JET SG (Standard grid) JET SG (Standard grid) JET EG [1] (Extended grid) JET EG [1] (Extended grid) [1] By S. Lisgo

Extended grid (EG)... to be filled with plasma

Conceptual approach DIVIMP Plasma transport of impurities ERODEPDIF: Flux balances ERODEPDIF: Flux balances Background plasma OEDGE (OSM) OEDGE (OSM) SOLPS (B2+Eirene) SOLPS (B2+Eirene) CARRE, recent codes CARRE, recent codes Grid Diffusion Sublimation Chemical phase formation Impurity generation SDTrim Materials properties Materials properties Material mixing model

Material mixing Plasma Each tile receives a flux due to erosion & re-deposition from other tiles Plasma transport is characterized by a re-deposition matrix: Flux of material m on tile i: Result: Set of n coupled differential / algebraic equations Concept: The first wall is divided into n tiles

Mixed material formation Plasma BulkReaction zone Background plasma Concept: Each tile is composed of a thin reaction zone and a bulk material Allows layer growth and erosion, sublimation and simplified chemistry. No diffusion! * Constant thickness Collision cascades: < 50 nm * Variable composition * Constant source / sink * Constant composition

Mixed material formation Bulk For n-tiles and k-chemical phases: kn coupled differential equations First tests with Mathematica: Works for >1000 coupled equations For n-tiles and k-chemical phases: kn coupled differential equations First tests with Mathematica: Works for >1000 coupled equations dσ X / dt = Plasma +Influx (by re-deposition matrix) – Erosion flux (by hydrogen and impurities) – Flux of sublimation (from vapor pressure of the chemical phase) ± Balancing flux (with bulk material) k Chemical phases or elements [X] [Y] [Z]... Chemical reactions +Flux of formation reactions (X is Product) – Flux of dissociation reactions (X is Reactant) Concept: Each tile is composed of a thin reaction zone and a bulk material

Prove-Of-Principle (w/o chemical reactions) Numerical solution for 69 tiles, re-deposition matrix and C wall + Be evaporation Initial Be coverage Re-deposition of Be

Prove-Of-Principle (w/o chemical reactions) Numerical solution for 69 tiles, re-deposition matrix and C wall + Be evaporation Initial Be coverage Re-deposition of Be Be is covered by C

Prove-Of-Principle (w/o chemical reactions) Numerical solution for 69 tiles, re-deposition matrix and C wall + Be evaporation [Be / Ǻ 2 ] Time [s] Tiles with Be at surface Tiles with C at surface All Be is covered by C

Conceptual approach DIVIMP Plasma transport of impurities ERODEPDIF: Flux balances ERODEPDIF: Flux balances Background plasma OEDGE (OSM) OEDGE (OSM) SOLPS (B2+Eirene) SOLPS (B2+Eirene) CARRE, recent codes CARRE, recent codes Grid Diffusion Sublimation Chemical phase formation Impurity generation SDTrim Materials properties Materials properties Model of surface chemistry

ITER first wall He Be W W C C O O H H N N Elements

ITER first wall He Nitrides: WN Be 3 N 2 Nitrides: WN Be 3 N 2 Hydrides: BeH 2 C X H Y OH 2 Hydrides: BeH 2 C X H Y OH 2 Carbides: WC, W 2 C Be 2 C Carbides: WC, W 2 C Be 2 C Beryllides: Be 2 W, Be 12 W Beryllides: Be 2 W, Be 12 W Oxides: WO 3 BeO CO 2 Oxides: WO 3 BeO CO 2 Be W W C C O O H H N N Elements Binary phases

ITER first wall He Nitrides: WN Be 3 N 2 Nitrides: WN Be 3 N 2 Hydrides: BeH 2 C X H Y OH 2 Hydrides: BeH 2 C X H Y OH 2 Carbides: WC, W 2 C Be 2 C Carbides: WC, W 2 C Be 2 C Beryllides: Be 2 W, Be 12 W Beryllides: Be 2 W, Be 12 W Oxides: WO 3 BeO CO 2 Oxides: WO 3 BeO CO 2 Be W W C C O O H H N N Tungstates: BeWO 3, BeWO 4 Hydroxides: Be(OH) 2, W(OH) X … Tungstates: BeWO 3, BeWO 4 Hydroxides: Be(OH) 2, W(OH) X … Elements Binary phases Ternary phases

Simplified description of ITERs first wall chemistry Be W C Be 2 C W 2 C WC Be 2 W Be 12 W Be gas BeO O ads WO 3 WO 3,gas Chemical phases Chemical phases 2 Be + C Be 2 C Be 2 C 2 Be + C W + C WC WC W + C 2 W + C W 2 C W 2 C 2 W + C W + 2 Be Be 2 W Be 2 W W + 2 Be W 2 C WC + W WC + W W 2 C Be + O BeO BeO Be + O W + 3 O WO 3 WO 3 W + 3 O Sublimation: Be Be gas WO 3 WO 3,gas O-Adsorption: O 2,gas O ads O ads O 2,gas Elementary reactions Elementary reactions … Equations for reaction fluxes Reaction balances Change of areal density of chemical phase = + all formation reaction fluxes – all dissociation reaction fluxes Couple to plasma transport code

Benchmarking example: W/Be/O XPS XPS experimental data 2.1 nm Be on W (Substrate,pc) mbar O 2 Layered system XPS experimental data 2.1 nm Be on W (Substrate,pc) mbar O 2 Layered system Model Model of coupled reaction equations Elementary processes: O adsorption Be and W oxidation BeO and WO 3 dissociation Be and WO 3 sublimation Be 2 W formation and dissociation Not included: Depth profiles (Homogeneous distributed phases) Model of coupled reaction equations Elementary processes: O adsorption Be and W oxidation BeO and WO 3 dissociation Be and WO 3 sublimation Be 2 W formation and dissociation Not included: Depth profiles (Homogeneous distributed phases)

Summary Set up a scalable model for JET (and ITER) that describes the first wall material evolution as a combination of: + Dynamic impurity generation (Parametrised TRIDYN) + Plasma transport via a static background (DIVIMP) + Some temperature dependent processes (Chemical phase formations, sublimation, directly benchmarked by XPS data) Method: Numerical solution of a set of coupled algebraic differential equations (Mathematica) Result: Time evolution of Surface concentrations (incl. layer growth) Plasma impurity concentrations Erosion and re-erosion fluxes Benchmark the results with JET experiments (e.g. post-mortem analysis of layers, spectroscopy of erosion fluxes)

Erosion and re-erosion by impurities Assumption: Individual sputteryields Y j of a mixture of elements scales linearily with the surface concentration Assumption: Individual sputteryields Y j of a mixture of elements scales linearily with the surface concentration Works well for Be / C but only fairly good for W / C, W / Be 50 eV D eV Be on C (Precalculated Yields)

Re-deposition matrix (JET SG) Promt re-deposition... Simple (unverified) OSM plasma background

Re-deposition matrix by DIVIMP Lauch flux of Be impurity ions and map points of re-deposition (Charge resolved) Re-deposition matrix, n ~ 70 static BGP Bin static BGP, standard grid